What are the solutions to the equation 2=x^3+x ?

The solutions to the equation 2=x^3+x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

Find the zeros of 2=x^3+x

The zeros of 2=x^3+x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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2 = x^{3} + x

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

2 = x^{3} + x

Switch sides

x^{3} + x = 2

Move

2

to the left side

x^{3} + x - 2 = 0

Factor

x^{3} + x - 2 : (x - 1) (x^{2} + x + 2)

(x - 1) (x^{2} + x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x + 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

9 x^{3} - 27 x^{2} = 0

2 x^{3} + 7 x^{2} - 16 x - 56 = 0

2 x^{3} + x^{2} - x + 3

3 x^{3} + 12 x^{2} = 0

x^{4} + 2 x^{2} = 15

What are the solutions to the equation 2=x^3+x ?
The solutions to the equation 2=x^3+x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of 2=x^3+x
The zeros of 2=x^3+x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2